A FIBER DAMAGE MODEL FOR EARLY STAGE …...synthesizing high quality composites from them [3]. To...

Pergamon Acta mater. Vol. 45, No. 3, pp. 973-986, 1997

Copyright 0 1997 Acta Metallurgica Inc.

PII: S1359-6454(%)00242-X Published by Elsevier Science Ltd

Printed in Great Britain. All rights reserved 1359X%54/97 $17.00 + 0.00

A FIBER DAMAGE MODEL FOR EARLY STAGE CONSOLIDATION OF METAL-COATED FIBERS

J. WARREN,? D. M. ELZEY and H. N. G. WADLEY Department of Materials Science and Engineering, School of Engineering and Applied Science,

University of Virginia, Charlottesville, VA 22903, U.S.A.

(Received 8 March 1996; accepted 27 June 1996)

Abstract-Recent studies of the high temperature consolidation of titanium alloy coated c+alumina fiber tows and BC monofilaments have both revealed the widespread occurrence of fiber bending and fracture during early stage consolidation. This damage was shown to arise from the bending of unaligned fibers during consolidation and was found to be affected by the mechanical behavior of the metal-metal contacts at fiber crossovers. To predict the incidence of fiber fracture during early stage high temperature consolidation, a time-temperature dependent micromechanical model incorporating the evolving contact geometry and mechanical behavior of both the metal matrix and the ceramic fibers has been combined with a statistical representation of crossovers in the pre-consolidated layup. The damage predictions are found to compare favorably with experimental results. The model has subsequently been used to explore the effects of fiber strength, matrix constitutive properties and the processing conditions upon the incidence of fiber fracture. It reveals the existence of a temperature dependent pressurization rate below which fracture is relatively unlikely. This critical pressure rate can be significantly increased by the ‘enhanced’ superplasticity of the initially nanocrystalline coating. Copyright 0 1997 Acta Metallurgica Inc.

1. INTRODUCTION

Continuous fiber reinforced titanium matrix composites (TMCs) possess combinations of specific modulus, strength, and creep resistance that are well suited for a variety of aerospace applications [l, 21. However, the pursuit of many of these applications is impeded by the high cost of TMCs. Significant fractions of this cost originate in the very expensive single monofilament silicon carbide fibers used for reinforcement and with the considerable difficulty of synthesizing high quality composites from them [3]. To reduce the contribution of the fiber to the composite cost, relatively inexpensive (sol-gel syn- thesized) cc-alumina fiber tows (e.g. the 112 or 410, 12 pm fiber filament Nextel 610TM tow) are being explored as an alternative TMC reinforcement [4,5].

One promising approach to composite synthesis using either fiber type involves first coating the fibers with thin protective layers to both reduce the deleterious chemical reactions between the fiber and the matrix alloy during subsequent high temperature processing and promote a low fiber matrix sliding stress. When sliding is able to occur at a relatively low stress (say - 100 MPa), relatively weak stress concentrations develop in the fibers adjacent to fiber breaks, and a global load sharing model predicted strength can be achieved [5,6]. Recent work has

tPresent address: General Electric, Coolidge Laboratory, 4855 W. Electric Avenue, W. Milwaukee, WI 53219, U.S.A.

explored several coating concepts for this including sacrificial TiB2 coatings as well as more complex (and more costly) diffusion inhibiting Nb/Y*O, duplex layers [_5, 71. To synthesize a composite from these protected fibers, the fiber tows or monofilaments are coated with the titanium matrix alloy using a physical vapor deposition (PVD) process such as electron beam evaporation [2,8-lo] or sputtering [ll, 121. The alloy coated tows/monofilaments are then packed into a suitably shaped container and consolidated to theoretical density using either hot isostatic or vacuum hot pressing [ 131.

The consolidation process has been shown capable of causing significant damage to the fibers, to the matrix and to the engineered fiber-matrix interface [5, 131. For example, if the cc-alumina fibers are not totally protected, the extended high temperature exposure during consolidation can result in local chemical reactions between the fiber and matrix. This can release a very large (matrix embrittling) flux of oxygen as well as weaken the fiber [5]. In addition, because the individual metal coated fibers within the a-alumina tows (or the SIC monofilaments in a random packing of metallized monofilaments) are not perfectly aligned, individual fibers can bend between crossover contacts and result in fiber fracture during consolidation (Fig. 1) [13-151. The bending and fracture are likely to reduce the effective strength of the fiber bundle [3, 51 and thus degrade the performance of the composite. The breaks also provide an additional pathway for chemical reactions

913

.*’ c’

e- .*

#=--__ t

--__

(4

: ..*. _I’

’ .- F “---_____

L

Fig. 1. Fiber bending and fracture resulting from consolidation of misaligned metal coated fiber (PVD Ti-6Al4V/a-alumina) aggregates: (a) polished section of a consolidated sample (HIP’ed 9OO”C, 100 MPa, 4 h); (b) view of damaged fibers after partial removal (etching) of matrix; (c) a schematic cross-sectional

view of a typical metallized fiber tow.

WARREN et al.: CONSOLIDATION OF METAL-COATED FIBERS 915

between the matrix and the fibers that may further embrittle the matrix.

Experimental studies of the fiber fracture have shown that failure occurs early during consolidation by excessive bending of crossing fiber segments that span contacts with other fibers, Fig. 1 [13, 151. These regions of fiber bending are established by the fiber packing geometry. As densification progresses, large stresses develop at the contacts between the crossing fibers. While this leads to desirable (densifying) inelastic matrix flow at the contacts, it also results in elastic bend stresses in the fiber span. For some spans, the stresses can exceed the (statistical) strength of the fibers before sufficient inelastic matrix flow occurs to infiltrate the void region between the fiber contacts and eliminate further bending [13].

The solution to this problem involves reducing the incidence of fiber crossovers (i.e. better fiber alignment) and decreasing the matrix resistance to inelastic flow. The latter can be accomplished if rapid creep at low stress is promoted either through the use of high temperatures or by exploiting the very small grain size frequently created in PVD alloys when deposited at intermediate temperatures [12]. The initial grain size depends upon the conditions used for vapor deposition (i.e. deposition rate, substrate temperature, etc.) of the matrix. The microstructure will subsequently coarsen at a rate that depends on the thermal cycle used for consolidation [13, 151. Since concurrent changes in relative density (which affects the contact stress and the bend cell span lengths), the matrix creep rate (due to rapid grain growth) and fiber strength (associated with diffusion through or dissolution of the protective fiber coating) and fiber strength (associated with diffusion through or dissolution of the protective fiber coating) accompanying consolidation, the fiber damage is likely to be a quite complex function of the initial matrix microstructure/fiber geometry and the consolidation process conditions.

Improved alignment of the metal-coated fibers shifts the distribution of fiber bend spans to longer lengths. The resulting improvement in processibility would have to be weighed against the additional effort of this approach, arising from the difficulty of producing tows containing aligned filaments, or in handling monolithic fibers and the need to control residual stresses (caused by nonuniform coating thickness) during matrix deposition. Our approach here is to explore processing strategies which would allow the production of high quality composite material using low cost (e.g. relatively poorly aligned) fiber preforms.

The goal is to develop a preliminary model that establishes the dominant ‘trends’ between fiber fracture and the consolidation conditions for PVD coated Nextel 610TM alumina fibers. In solving the problem, the geometry and micromechanics are simplified so that reasonably tractable solutions can be obtained. The model combines an analysis of the

bending of a representative span due to viscously deforming contacts with a measured initial span length distribution. Time/temperature dependent creep properties for the microstructurally evolving matrix are then used to compute a time dependent distribution of bend stresses within the layup during the early stage consolidation (where most damage occurs). These stresses are combined with Weibull fracture statistics for the fiber to determine an overall fiber fracture probability and thus, a fiber fracture density (i.e number of fractures/meter of fiber). This is compared with earlier experimental results [ 131. The verified model is then used to identify the trade-offs between pressurization rate and consolidation temperature that minimize the fracture problem. The model predicts that provided good chemical protection of the fibers can be achieved, acceptable levels of fiber fracture can be accomplished during densification of these tow-based materials. We find this to be enabled by the unusually high creep rate of the fine grain size PVD matrix alloy. The model is equally applicable to the consolidation of metallized SIC monofilament arrays and indicates that similar consolidation strategies could also be applied there.

2. FIBER FRACTURE MODEL

The goal of consolidation is to cause the metal matrix to laterally flow and fill the void regions in (see Fig. l(c)), while avoiding fiber crossover contact stresses high enough to cause a significant probability of fracturing the alumina fiber (or SIC monofilament). The model is needed to explore how the extent of fiber damage (the model output) depends upon the packing of the metal coated fibers, the resistance of the matrix to flow, the bend stiffness and strength of the fibers, and the process conditions (i.e. the temporal variation of the consolidation pressure and the temperature). A similar statistical micromechan- its approach was used by Elzey and Wadley [16] to model the evolution of fiber damage during the consolidation of MMC monotapes produced by induction coupled plasma spray deposition. In that system, fiber microbending resulted from surface roughness, a characteristic of the plasma sprayed tape. In the case, as the MMC monotapes were pressed together during consolidation, localized stresses developed where asperities contacted adjacent plies and caused fiber bending. While changes in the matrix microstructure of plasma spray deposited metals/alloys has not been incorporated in the previous models, this evolution cannot be ignored in the present case of PVD matrix coated fibers.

2.1. Model formulation

Experiments have shown that the initial relative densities of metal coated Nextel 610TM tow or SIC monofilament layups prior to consolidation lie between 0.45 and 0.55 [13, 151, significantly less than the 0.9 1 relative density of a hexagonal close packing

976 WARREN et al.: CONSOLIDATION OF METAL-COATED FIBERS

a) Idealized architecture

I \ M$,~~,$$wo!$d Fiber Void

Z b) Representative cell L -“F Y

c) Cell deformation

Consolidation pressure

Matrix plane strain flow

Fig. 2. Idealized cellular solids architecture used to simulate early stage densification and fiber fracture during consolida-

tion processing.

of uniform diameter fibers. This arises from fiber crossover caused by misalignment created during synthesis of the tow (and its random packing for consolidation), and fiber bending upon cooling after metallization (due to non-uniform metal coating thickness). This creates a preconsolidation fiber architecture of the form shown schematically in Fig. l(c).

Our objective is to predict the number of fiber fractures which occur per meter of fiber length as these metal coated fiber aggregates densify during consolidation. We take a micromechanics approach in which a unit cell is first identified whose behavior can be used to respresent the overall aggregate. This unit cell (Fig. 2(b)) is chosen to consist of a segment of coated fiber and three matrix contacts with neighboring fibers. The random nature of the structure illustrated in Fig. l(c) (with fibers crossing at various angles) leads to a type of cellular structure characterized by a distribution of cell lengths. Since the force required to deflect a fiber depends on the fiber’s span length, a unique stress-strain response is associated with each of the cells in the distribution.

The overall response will therefore be the sum of the responses of the cell distribution.

The macroscopic structure of the aggregate can be approximated by allowing the unit cells to repeat in a three-dimensional space, creating a ‘cellular’ structure similar to that discussed by Gibson and Ashby [17]. Analysis of each unit cell predicts the forces required for early stage densification and also captures the interaction between the creeping matrix and the (predominantly) elastic fibers that bend and fracture. Considerable simplification could be achieved if the variously sized cells were able to be replaced by the same number of identical (average) cells (i.e. the usual micromechanics approach). However there exist two obstacles to this. Firstly, the elastic-nonlinearly viscous behavior of a cell like that shown in Fig. 2(b) results in a path-dependent stress-strain response. An array of different span length cells deforming in parallel cannot be modeled using a single cell. Secondly, no single ‘average’ cell could describe both the densification and fiber fracture behavior since these two processes exhibit different (nonlinear) dependencies on cell length [16, 181.

Our approach is to therefore discretize the cell size distribution, model the behavior of a finite number of cells with different span lengths deforming in parallel, weight each cell by its probability of occurrence in the cell population, and obtain a weighted sum of the responses. The resulting model structure in two dimensions is shown in Fig. 2(a), which represents the y-z plane in Fig. l(c). Analysis of the problem is complicated for a general state of consolidation stress. Rather than attempt a multiaxial constitutive model for the overall behavior, we restrict the development to uniaxial macroscopic deformations (in the z-direction in Fig. l(c)). The resulting model is expected to provide a reasonably accurate simulation of densification and fiber damage during vacuum hot pressing (VHP) and to be approximately valid for the HIPing of a sheet-like geometry where most deformation occurs through the thickness.

The overall fiber fracture evolution during consolidation is obtained by: (i) applying the processing pressure (at the elevated processing temperature) to a unit cell array; (ii) allowing a consolidation strain to develop in each cell (with stresses satisfying equilibrium with the applied stress); (iii) determining the probability of fiber fracture in each cell; (iv) weighting each cell by its relative frequency; (v) summing the weighted fracture probabilities of all the cells in the ensemble.

2.2. Macroscopic relations

Suppose a time dependent processing pressure, P(t), is applied to a metallized fiber layup like that shown in Fig. l(c). If the layup is contained in a die (as for example in vacuum hot pressing), a macroscopic strain occurs in the direction of the applied stress (with the lateral strains being zero).


Although local variations in uniaxial strains can occur, we assume that macroscopically, isostrain conditions apply (i.e. planes perpendicular to the macroscopic strain remain plane). For such a uniaxial deformation, the macroscopic behavior can be inferred from the response of any of the 01-z) planes such as that shown in Fig. 2(a), provided it contains a reasonably large (representative) number of unit cells. The analysis can be further simplified to a single row of cells if the length, L, of the plane under consideration is much greater in the fiber direction than the average cell length, again to ensure a representative cell population. This condition being satisfied, the analysis of just a single row of cells will be representative of the behavior of the three-dimensional array.

Suppose a total of N cells exist in a row. If the probability of finding a cell of length between 1 and I+ dl is 4,(l) dl, then the distribution of cell lengths can be described by a probability density function (PDF), 4,(l), and the average cell length, 1, will be defined by its first moment

If the cells are taken to be of width, && (where dr is the fiber diameter and 19 is a packing factor chosen such that the cells are volume-filling in the x-direction, Fig. l), the average area occupied by the cells is

The force acting on the cells whose area is given by equation (2) is related to the applied stress by

F(ct) = P(t);l. (3)

Enforcing equilibrium between the applied force and the local forces acting on the cells (1c,) gives

F(t) = s L q,(l) . F,(f, h, t) dl (4) II

where h is the unit cell height. The cell height is related to the relative density, D,

of the composite, which is a function of the applied stress and can be expressed as D = G(P, t), Since all planes (made up of unit cells) perpendicular to the applied stress are identical, the relative density of any one of these planes is the same as that of the composite. The macroscopic relative density is then related by conservation of volume (due to the incompressibility of both fiber and matrix) to the thickness (in the z-direction), h,, of a single (arbitrary) (x - y) plane subjected to constrained uniaxial compression by

h =!%!a P D

where ho and D,, are the initial plane thickness (i.e. cell height) and density, respectively. Since the plane is assumed to deform under isostrain conditions, the height of any particular unit cell, h, must be the same as for all others; therefore h, = h. With the unit cell height, h, thus related to the composite density, it can be seen that the equilibrium equation (4) also provides the overall constitutive response, i.e. a relation between the applied stress and composite density. With the applied force in equation (4) given and the cell length distribution, 4,, measured [13], the next step is to relate the force acting on a unit cell, F,, to its length, 1 and height, h.

2.3. Unit cell analysis

The time-dependent deformation occurring at the contact between two metal coated fibers which cross at some angle during consolidation is a complicated inelastic flow problem which has not as yet been investigated. The unit cell, shown in Fig. 2(b), is clearly an idealized representation of the geometry present in the actual material. The contact has been idealized as a rectangular asperity with dimensions, z,y,&. As force is applied to the cell, the cell height, h, decreases because of contact deformation (decrease in asperity height, zC) and due to deflection, A, of the fiber. From Fig. 2(b), it can be seen that the unit cell height, h, depends on the extent of contact deformation and fiber deflection, and is given by h(t) = 22,(t) + df - A(t), which, when differentiated with respect to time leads to

h = 22, - A. (6) The rate of change of contact height, i,, is

determined by the contact stress, a(t), and by the constitutive response of the matrix. Since significant pressure is normally applied only after the layup has been heated into a regime of rapid creep, it is assumed that the strain-rate of the matrix can be represented by a power law constitutive relation for steady-state creep. Since the matrix exhibits significant grain coarsening during consolidation, we use a constitutive model that explicitly incorporates the grain size. Warren et al. [12] found that for uniaxial deformation, the strain rate of the PVD matrix coating could be well represented by

i = &, e-Qi(Rn. !? dp

where Q is an activation energy for creep, B,, is a temperature independent creep parameter, n is the creep stress exponent, d(T, t) is a temperature, time-dependent function which describes the instantaneous matrix grain size (see Table l), p is a grain size exponent, T the absolute temperature and R( = 8.315 J/(mol K)) is the universal gas constant. The contribution of plastic deformation and transient creep are ignored in such an analysis. They effectively reduce the deformation resistance of the contacts for a fixed loading rate so the steady state creep


assumption equation (7) is likely to result in a (conservative) overestimate of the predicted fiber damage.

Approximating the uniaxial contact strain rate as i = ie/zo equation (7) can be used to write the contact deformation rate

Q”

Since the contact and the fiber are in series (i.e. the applied force is transmitted through the contact to the fiber), the force acting on both elements is just the force applied to the cell. The stress acting over the contact area, a,, is related to the force by cr = F,/u,. As the contact deforms in the z-direction, incompressibility requires that lateral (x and y) deformations conserve volume. Again in the interest of arriving at the simplest mathematical formulation which preserves the essential physical phenomena, lateral strains are considered to take place only in the y-direction, Fig. 2(c). Conservation of volume then leads to

yczc = y,z, (9)

where y% and z,~ are the initial asperity width and height, respectively. The contact area, given by a, = y,(t)& can then be expressed in terms of z,

a, = y, 2 df. (10)

With equation (lo), equation (8) becomes an ordinary differential equation in z,.

The fiber is assumed to experience only elastic deformations, although the elastic modulus, Er, is treated as a function of temperature. The fiber deflection (Fig. 2(c)) is related to the cell force (from elementary beam theory) by

F, = k, A

where k, is the bend stiffness

(11)

k,(t) = s s (12)

where /$(t) is the length of the fiber span subject to bending, which changes with time because of lateral spreading of the contact. The bending span length is expressed as IS(t) = I- ye(t) = I- yszs/ze(t). The contribution of the metal coating to the fiber bend stiffness will usually be small and has therefore not been included in equations (11) and (12).

2.4. Composite densiJication model

The composite stress-strain response can now be specified by the equilibrium equation (4), the contact constitutive equation (8) and equation (6) for relating the rate of change of cell height to the fiber deflection rate. These can be expressed as a system of three, nonlinear differential equations in F,, z, and h.

d L P = Z o (q,(l) . Fc(f, h, 0) df

s (13)

Table 1. Mechanical properties of the NEXTEL a-alumina fiber, the PVD and conventionally processed Ti-6Al-4V alloy.

a-Alumina fiber properties Symbol Value Ref.

Diameter (pm) Young’s modulus 1 (MPa) Reference strength* (MPa) Weibull modulus

Temperature independent creep parameter (m (MPa)-” s-i) Activation energy for superplastic flow (kJ mol-r) Creep stress exponent Grain size exponent Grain growth exponent at 76O”Cp Grain growth exponent at 840°C Grain growth exponent at 900°C Grain growth constant at 760”Ct (pm sp) Grain growth constant at 840°C (pm SK’) Grain growth constant at 900°C (pm s-‘) Initial grain size at 760°C (pm) Initial grain size at 840°C (pm) Initial grain size at 900°C &m)

Creep stress exponent Grain size exponent Temperature independent creep parameter (m (MPa)-” SK’) Activation energy for superplastic flow (kJ mol-I)

dr 12 El 390,000 00 2380 m 9

PVD Ti-6Al-4V matrix propertiesf BO 0.00003

Q 140

n P (I a

: k

:

1

Conventionally processed Ti-6Al-4Vf n P BO

Q

1.4 1 0.24 0.20 0.20 0.14 0.23 0.23 0.11 0.20 0.50

1.67 [2X 241 0 W241

19.9 P, 241

153 W241

[51

t:j 151

WI

WI

WI

[ii; P21 WI

t:;\ WI WI

tt;;

tPrior to consolidation processing $A11 material parameters shown apply to equation (8) in the text. gApplies to a grain growth relationship of the form, d[t] = do + kta.

WARREN et al.: CONSOLIDATION OF METAL-COATED FIBERS

”

Equation (13) is an integro-differential equation obtained as the time derivative of equation (4). Equation (14) is obtained from equation (8) with the substitution, cr = FJac = Fcz,/y,z,,df, and equation (1.5) was obtained by differentiating equation (6) and making appropriate substitutions using equations (8Hl2). Their solutions are constrained by the isostrain condition that requires the cell height, h, be independent of cell length, 1. This is satisfied if all cells deform at the same rate for all t > 0:

^ ;/;=o. (16) Equations (13)( 16) provide a basis for calculating

the densification rate of an aggregate of misaligned, metal coated fibers during consolidation at elevated temperatures. The model requires constituent material parameters, BO, Q, p, n, Ef and df (which may be treated as time- and/or temperature-dependent quantities if data or models for their evolution are available) and the fiber span length distribution, $,, controlled by the process used to manufacture the coated fibers and by the manner of their packing.

2.5. Fiber damage model

The overall deformation (as given by the cell height, h(t)) for a given applied stress is obtained by solution of equations (13)-( 16), which also yields the contact heights, z,(t). The fiber’s deflection, A, within any given cell of length, 1, is then found from equation (6), which is subsequently used to determine the stress in the fiber. Many different bending geometries could occur. We calculate the maximum tensile fiber stress (of) by analyzing a cylindrical, elastic beam subjected to symmetric three-point bending assuming fixed end constraints [19]

(17)

The time dependence of the stress arises from both the time dependence of the deflection and the cell length. The ceramic fibers used for metal matrix composities typically exhibits time independent fracture strengths in tension which can be described by a Weibull distribution. However, the time dependence of the span length and fiber stress results

in a time-dependent fiber survivability, Y(t), for an arbitrary cell is then given by [20]

Y.[t]=exp[-rci(,>-] O


Consolidation pressure p

P Fig. 3. The macroscopic densification/damage behavior is modeled as an ensemble of unit cells, each of which is described by a single Maxwell element. Springs represent the elastic deflection of the fibers, while the dashpots model the viscous (power-law creep) deformation of contacts at fiber

crossovers.

inserted into equation (18) to determine the probability of survival within each fiber segment (cell). Finally, the overall fiber damage is calculated by integrating the probabilities of fracture (1 - survivability) over all cells (equation (21)). A numerical solution procedure has been developed as described below.

3.1. Discretization

The densificatiomdamage model embodied in equations (13x21) is based on a continuous distribution of cell lengths. A numerical implemen- tation will be used in which c#@) is replaced by a discrete distribution containing N unit cell lengths. The composite unit cell behavior given by equations (6x12) is that of a Maxwell element in which a linear spring (bending fiber) is placed in series with a nonlinear viscous dashpot (matrix creep at contacts). The overall behavior can then be modeled as an array of N Maxwell elements, all undergoing the same uniaxial displacement rate, 8, Fig. 3. While all cells are required to have the same height, the load they each support as well as their fiber deflection and contact deformation will all be different.

Replacing the integral in equation (13) with a summation, thereby reducing the analysis to a finite number of fiber bend cell lengths, gives

where N is the number of different cell lengths considered (i.e. the number of bins into which the entire range of cell lengths are divided), J; represents the number fraction of cells of length, Z,, and &, is the rate of change of contact force acting on a cell of length, Zi. The contact height, ze, and cell height, h, are still given for each cell type by equations (14) and (15), respectively. In addition, the isostrain condition (16) is satisfied by having the rate of change of height of each cell be equal to that of the plane containing all the cells, fi

iii = A. (23)

The 3N + 1 system of equations (equations (14), (15), and (23) for each of the N cell types plus the equilibrium equation (22)) were programmed using MathematicaTM [22] and solved with an adaptive stepsize, fourth order Runge-Kutta ODE integration scheme.

The overall fiber survivability is obtained by replacing the integral in equation (20) with a discrete summation

Y(t) = 2 “A$& t). (24) i=,

Similarly, the discrete approximation of the fiber fracture density, p, obtained from equation (21) is

3.2. Unit cell distribution

It has been assumed that a composite layup will contain a distribution of cells like the ones described in Section 2.1. The cell length distribution used for this simulation was determined by a detailed metallographic analysis of preconsolidated specimens, Fig. 4 [13]. This is a very broad distribution requiring many cells to be included in the analysis and thus extensive computation. To simplify, we note that when the matrix of consolidated samples was dissolved by acid etching, roughly 60% of the fiber segments in the sample were of length ~70 fiber diameters, suggesting that the bending mechanism responsible for fiber breaks is active over a distribution of cell lengths much narrower than the one depicted in Fig. 4 [ 131. The very long cell lengths

C .G 0.07

‘i,

s 0.06

iii 0.05

f 0.04

z’ 0.03

0.02

0.01

0.00 I . i loo 200 300 400 500 800 700

e ldf

Fig. 4. The measured distribution of unit cells (fiber bend segment lengths) in a sample prior to consolidation.

WARREN et al.: CONSOLIDATION OF METAL-COATED FIBERS

Table 2. Physical dimensions of each unit cell type

Cell type lldr L(O)/dr ywldr z=oidt 1;

981

1 8.50 2 10.00 3 12.50 4 15.00 5 18.75 6 24.00 7 28.00 8 36.25 9 41 .oo

10 45.00 11 54.00 12 70.00

6.2 8.5

10.6 12.7 16.0 20.4 23.8 30.8 34.9 38.2 45.9 59.5

1.3 0.7 0.046 1.5 0.7 0.039 1.9 0.7 0.036 2.3 0.7 0.072 2.8 0.7 0.128 3.6 0.7 0.056 4.2 0.7 0.171 5.4 0.7 0.020 6.1 0.7 0.095 6.8 0.7 0.027 8.1 0.7 0.023

10.5 0.7 0.283

shown in the distribution will likely interact with nearest neighbor fibers during consolidation, re- arrange and form additional contacts so that few fractured segments of this length are found after consolidation. Thus experiments indicate (and our subsequent model analysis reveals) that fiber segments of length, I> 7Odf, do not appear to be very important. In addition, very short fiber segments, say I < 4-6dr, must be excluded from the analysis since they possess very high stiffness in bending and are unlikely to fracture by a bending mechanism. Therefore we truncate the distribution of cell lengths, $I(09 consider only cells within the limits, 8.5dr < I< 7Odr and obtain a computationally efficient solution.

3.3. Process simulation methodology

In practice, consolidation process schedules are usually used in which temperature is first increased, followed by the application of pressure once the temperature has reached a constant (soak) value. Although more complicated cycles could be used as input, the isothermal process schedule is adequate for exploring the factors affecting fiber damage evolution. The fiber fracture simulations were carried out in the following steps: (1) selection of a consolidation temperature, T, and pressurization cycle, P(t); (2) determination of the lengths of the cell types, l,, and the number fraction of each type in the ensemble, f;, (from experimental data); (3) selection of the appropriate matrix and fiber properties (i.e. the modulus and Weibull parameters for the fiber and the temperature dependent matrix creep and grain parameters); (4) simultaneously solving the loading rate relationship, equation (22) and, for each cell type, the three governing differential equations that determine their coupled, micromechanical response, equations (14), (15) and (23) (the contact height relationship, the cell height relationship and the isostrain condition, respectively). The simulations presented below are based on the simultaneous output response of 12 unit cell types ranging in length from 8.5dr to 70df (see Table 2). A system of 37 (3N+ l), first order, ordinary differential equations were solved to determine, for each cell type, the fiber bending stress (equation (17)), fiber

survivability (equation (18)) and the cumulative ensemble survivability (equation (24)).

The model in its present form can be used for predicting early stage fiber damage, to densities D m 0.75. This corresponds to the density value when some of the fiber segments deflect beyond the geometric bounds of their respective cells. The elastic deflection of fibers into the void space between crossover contacts is interpreted here as stage 1 consolidation behavior. If needed, a subsequent stage 2 consolidation model could treat the formation of new contracts along the bending fiber segment resulting in cell division.

4. SIMULATION OF FIBER FRACTURE

To investigate the model validity, a detailed simulation has been performed for two previously reported process cycles, designated VHP-1 and -2 (Fig. 5) conducted at a consolidation temperature of 840°C [13]. For these experiments, the metal coating around the fiber was a uniform 4.2 pm in thickness for a resultant matrix volume fraction of 0.65. The cycle VHP-1 had been designed (using this model) to have a loading rate that would not significantly fracture fibers. The VHP-2 cycle used a more rapid loading rate, typical of current consolidation practice. The fiber fracture densities were measured experimentally for both tests and are described in

IO I I I 840% /I

Time (set)

Fig. 5. Vacuum hot press consolidation process cycles: VHP-2 is typical of conditions used to consolidate metallic powders, while VHP-1 is a cycle designed for consolidation

of metal coated fibers.


Time (set)

Fig. 6. Calculated fiber bending stresses developed during the (a) VHP-2 and (b) VHP-1 process cycles.

[13]. The initial and final densities of the specimen in each simulation were identical (0.48 and 0.73), respectively.

The initial contact height, z;, = 0.7dr (8.4 pm), represented the initial thickness of matrix material located between adjacent crossing fibers. An initial contact length of YiO = 0.151, was selected to obtain an initial cell density of 0.50 which was similar to the initial packing density of the preconsolidated specimen. The grain size dependent, constitutive properties of the matrix material were those measured for the superplastic PVD Ti-6A14V alloy coating and are given in Table 1 [12]. The measured mechanical properties of the fiber are also given in the table. It has been assumed for each simulation that the fiber reference strength, rrO, was a function of temperature only [5]. This is equivalent to assuming the fiber remains fully protected from the matrix.

Consider first the bending stresses generated in the fibers due to the VHP-2 simulation shown in Fig. 6(a). Since each cell in the ensemble experiences the same compressive strain (i.e. the isostrain assumption imposed by equation (23)), the applied processing load is supported initially by the stiffest cells (the cell types of length 8.5dr and 1Odr in the figure). These relatively short, stiff cells contain fiber spans that do not readily deflect resulting in relatively low bending stresses in the fibers. The contact stresses developed in these cell types are consequently large and result in extensive viscoplastic contact strain, densification of the cell, and thus rapid additional stiffening. As the shorter cells stiffen, they become progressively capable of supporting larger loads

without breaking the fibers they contain. The longest cells (of length 54df and 70df in Fig. 6(a)) have a low initial bending stiffness, allowing the fibers to deflect readily when loaded. At the start of the process cycle these long cells support virtually no load and experience a low fiber bending stress. As the process pressure increases, the load in the long cells begins to increase but at a much slower rate than other shorter cells in the population. The longest and shortest cells in the ensemble have the lowest bend stresses, Fig. 6(a) and are therefore least likely to contain breaks Fig. 7(a).

Reducing the loading rate decreases the densification rate and thus results in smaller cell contact forces, reduced fiber bend stresses and less fiber fracture. For example, in the VHP-1 simulation, the processing pressure was applied much more slowly, allowing significant time for creep densification to occur. The maximum fiber bending stresses predicted using VHP-1 (shown in Fig. 6(b)) are seen to be less than half the bending stresses predicted using the VHP-2 pressure cycle and resulted in a significantly higher fiber survivability, Fig. 7(b). The nonlinearity of the fiber strength distribution amplifies this. The ensemble survivability (i.e. the cumulative number fraction of cells containing breaks) indicates a tenfold reduction in fractures, Fig. 8. Each figure shows the instantaneous number fraction of cells in the ensemble likely to contain breaks. The VHP-2 simulation predicts approximately 48% of the ensemble members are likely to contain breaks after processing to a final relative density of 0.75 compared to 2% for the VHP-1 simulation. This equates to 950

0.6

60 a0 1 .o

$ 0.8 - f/d,=41 -/

.s ; 0.6 -

.r 2 0.4 - z = al 0 0.2 -

0.0 ’ I I I I I 1 0 200 400 600 800 1000

Time (set)

Fig. 7. Fiber survivability for various fiber bend (unit cell) lengths for the (a) VHP-2 and (b) VHP-1 process cycles.

0.7

0.6

0.5

0.4 1 I I 1 1 0 20 40 60 60

o 9 (b) VHP-I .c

Simulation: S8 fractures/m 0.8 Experiment: 120 fracturBS/m

0.7 t 1

0.41 I I I I I

0 200 400 600 800 1000

Time (set)

Fig. 8. Cumulative number fraction of cells containing breaks for (a) VHP-2 and (b) VHP-1 process cycles. When multiplied by the number of cells, the VHP-1 cycle is predicted to result in 88 fractures/m (120/m measured) while VHP-2 was predicted to have 950 breaks/m (compared with

600/m measured).

and 88 predicted fiber fractures per meter of fiber in VHP-2 and VHP-1, respectively and compares relatively favorably with the 600 and 120 measured breaks per meter for VHP-2 and VHP-1 [13].

The model appears to overpredict the degree of damage caused by the process cycle VHP-2. The discrepancy may be due, in part, to the onset of stage 2 deformation early in the densification cycle resulting in limited bending fractures, and neglect of the deformation associated with both matrix plas- ticity and transient creep. These reduce the deformation resistance of the contacts and are likely to result in less severe fiber deflection. The model also

10 MPalh

150 MPalh

0

density of 0.75.

n Critfcal pressurization

L( J,‘J rates for no damage

1.0, \’ I * 0.9 t .z? x 0.8 -

.$ 0.7 -

5 0.6 -

ii 0.5 - E E 0.4 -

$ 0.3 - w

0.2 1 I I 1 10 100

Pressure ramp (MPa/h)

Fig. 11. Cumulative overall fiber survivability as a function of (constant) pressurization rate for selected fiber reference

strengths.

100 200 300 400 500 600

Time (set)

Fig. 9. Cumulative overall survivability (i.e. processibility) for four constant process pressurization rates at a consolidation temperature of 840°C and a final relative

Fiber reference strength (GPa) = 1.2

200 400 600 800 1000

Time (set)

Fig. 10. The influence of the fiber’s reference strength on cumulative overall fiber survivability for the VHP-1 process

cycle.


somewhat underpredicted the damage caused by the VHP-1 processing cycle. The inconsistency may be due to a gradual reduction in the fiber reference strength as a result of chemical attack by the matrix. Fibers removed from consolidated specimens by acid etching of the surrounding matrix exhibit surface pitting, indicative of reactivity with the matrix [13]. The effect of fiber reference strength is considered further in Section 5.

5. THE EFFECT OF PRESSURIZATION RATE

From the results presented above, fiber failure during consolidation is seen to be sensitive to the rate of loading which governs the overall densification rate, local contact pressures, and thus fiber bend stresses. Figure 9 shows the predicted cumulative survivability (i.e. the processibility) for four constant pressurization rates of 150, 100,50, and 10 MPa/h, all imposed at 840°C. The initial and final relative densities of each simulation were identical (0.48 and 0.75, respectively), and the material properties of the matrix and the fiber were those given in Table 1. The figure shows that rapid pressurization rates result in extensive fiber fracture.


P i.o.,,,.-_- , -\

E VHP-1 ‘\

PVD alloy

T = 040% ‘\ D= 0.75

z ‘1

\

cd 0.9 - \

2 \ \

2 \ \

2 Cmmtlonal “S

$ 0.8 - SUperplaStiC : TI-BAI-4V alloy - 0~0.72

Iii

0.7 1 I I I I I 0 200 400 600 800 1000 1200

Time (set)

Fig. 12. Processibility (i.e. fiber survivability) is enhanced by using the PVD Ti-6Al4V matrix due to its ultrafine grain size which gives rise to enhanced superplastic

behavior.

We can use the densification/damage model to explore the influence of the fiber’s reference strength on the susceptibility to fiber failure, as shown in Fig. 10. The cumulative ensemble fiber survivability for the process cycle VHP-1 is shown as a function of time for various fiber reference strengths. (Here, the cell distribution, the mechanical properties of the fiber, and the visco-plastic properties of the matrix are unchanged.) In Fig. 11 the cumulative fiber survivability for a range of fiber reference strengths, eO, is shown as a function of (constant) pressurization rate. We note the existence of a critical pressurization rate below which negligible fiber damage occurs. This pressurization rate is a strong function of the fiber strength (doubling the strength allows a ten-fold increase in pressurization rate). From this it is clear that: (1) high fiber reference strengths are necessary to avoid fiber fractures (and efforts to develop stronger fibers will be beneficial from a processibility standpoint), (2) fiber damage is very difficult to avoid with the fibers used in this simulation unless low consolidation loading rates are maintained during the early stages of densification. Finally, for a fixed pressurization rate, a 20% drop in the fiber reference strength (from 2.0 to 1.6 GPa) results in a 20% increase in the number of fractures, again emphasiz- ing the need for high strength, damage resistant fibers.

6. PROCESSING WITH A PVD MATRIX

The process simulations above indicate that fiber damage can practically be eliminated even in poorly aligned fiber tows if optimal process conditions are chosen. However, the flow properties of the metallic matrix, which determine the relative ease of contact flow (leading to densification) or fiber deflection (leading to fracture), are clearly very important. It is informative to substitute the constitutive response of a conventional Ti-6A1-4V alloy for that of the PVD matrix and to explore the extent to which the nanocrystalline structure of the vapor deposited matrix affects processibility.

The constitutive properties of a conventionally processed Ti-6Al-4V alloy in the 750-900°C temperature range can be determined from the combined experimental data of Arieli et al. [23] and Pilling et al. [24] (see Table 1). Two separate simulations using the VHP- 1 process conditions were then conducted; one with a conventional (superplastic) Ti-6Al4V alloy and the other with the PVD alloy. The cumulative fiber survivability for each simulation are compared (Fig. 12) together with the final density reached. The figure shows that the PVD matrix alloy achieved a higher density in a shorter time and with significantly less fiber damage. This arises from the submicron grain size of the PVD alloy since the strain-rate varies inversely with grain size and is significantly enhanced for the PVD microstructure [12]. Although rapid coarsening accompanies consolidation at 840°C [12], the grain size of the PVD alloy still remains about a factor five less than that of the conventionally processed material.

Critical pressurization rates for no damage

I * I111111 , 9 0.9 - ‘\ 0 ‘\ ‘\ % 0.0 - ‘\ .g 0.7 - ‘\

‘\ ’ ‘\ z 0.6 - Cwwentional superptasti~*‘.,

al 0.5 - E E 0.4 -

3 0.3 - w (a) T= 760°C 0.2. * ~~‘~~‘~( ’ “‘,a,,’ ’ “‘~~*~’

0.1 1.0 10.0 100.0 1.0

9 0.9 E z 0.8 .g 0.7

’ 3 0.6

a 0.5 B E 0.4

8 15 0.3

0.2

1.0

* 0.9 0 z 0.0

.g 0.7

’ 7 0.6

a, 0.5 B 5 0.4

g 0.3 W

0.2

Conventional supefplastic~‘~,~

- (b) T= 040°C I I

1 10 100

- (0) T= 900°C 1 I

1 10 100

Pressure ramp (MPa/h)

Fig. 13. Overall survivability as a function of pressurization rate for three different processing temperatures. The two matrices are comparable at the highest processing temperature due to rapid grain growth in the PVD matrix.


E ; 14 1 1

g 12- TMAI-4V D= 0.75

a lo- E P"D/ : I'

,' ,'

I' a'

Conventional supeiplastic _ *’ In

8? 2- ___--- __-' __.*

a 3 -

o ______----- I .$ 750 800 850 900 'C 0 Temperature (“C)

Fig. 14. Critical pressurization rate (defined as the rate for which no damage occurs) increases with processing temperature and is a factor of 2-10 greater for the PVD

TiAAl4V matrix.

In Fig. 13(aHc) the ‘processibility’ of the PVD alloy is compared to that of the conventional alloy for a range of consolidation temperatures and pressurization rates. The model predicts that improved processing behavior can be achieved by using the PVD matrix material, which readily creeps under the consolidation conditions simulated here. The critical pressurization rate for avoiding damage also im- proves. In Fig. 14 the critical pressurization rate for both the PVD and the conventional processed alloy, is plotted as a function of the consolidation temperature. The figure again shows that the enhanced creep behavior of the PVD alloy allows significantly higher pressurization rates to be used during consolidation. As the processing temperature is increased, the difference between conventional and PVD alloy processibility disappears due to concurrent grain growth in the PVD material.

The effects of loading rate and consolidation temperature are summarized in Fig. 15. Fiber damage

+---- Increasingdamage

I I 800 850

Temperature (“C)

Fig. 15. Contours of constant overall fiber survivability as a function of consolidation processing conditions. Low pressurization rates and higher temperatures favor matrix flow at contacts rather than fiber deflection (and fracture).

is minimized when the pressurization rates are low and the processing temperature is high, (conditions favoring matrix flow at contacts as opposed to fiber bending). It must be kept in mind that although consolidation temperatures promote matrix deformation, the accelerated reaction kinetics at the fiber-matrix interface may result in unacceptable loss of fiber strength unless good protective coatings have been previously applied to the fibers.

7. CONCLUSIONS

A micromechanical model for predicting the extent of fiber damage during the elevated temperature consolidation of PVD metallized fibers has been developed and applied to the consolidation of PVD metallized NEXTEL 610 a-alumina tows. The model incorporated creep contact deformation, elastic fiber bending/fracture and grain growth during consolidation. It predicts levels of damage (and a dependence on loading rate) which are similar to those of the experimental results. The model has been used to investigate the sensitivity of the damage to the consolidation processing conditions and fiber/matrix properties. It has been found that the rapid pressurization rates typically employed to consolidate metal powders are unsuitable for consolidating metal coated ceramic fiber composites and result in extensive fiber fracture even when the compacts are fully heated before application of pressure. The simulations indicate that fiber damage can be avoided by increasing the temperature and lowering the pressurization (densification) rate during the early stages of consolidation: the optimal conditions will depend on the fiber’s strength, its protective coating integrity and the elevated temperature creep properties of the matrix alloy. A critical pressurization rate has been found, below which damage is unlikely. The relatively low amount of fiber fracture predicted for this system arises from the enhanced superplasticity of the PVD alloy matrix.

Acknowledgements-The authors would like to thank Messrs H. Deve, J. Storer, R. Kieschke, and P. DeBruzzi of the 3M Metal Matrix Composites Center for their advice and assistance. This work has been supported by the Defense Advanced Research Projects Agency (W. Barker, Program Manager) and the National Aeronautics and Space Administration (D. Brewer, Program Monitor) and the DARPA URI through UCSB.

1. 2.

3.

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